Mathematics for the interested outsider

Fundamentalist physics

UPDATE: I originally phrased my closing sentence poorly, and have chosen to revise it. The original should remain, struck through

I’d been hoping to write about today’s entry in the department’s graduate student seminar today, but there wasn’t a speaker lined up. So I guess I’ll have to get my rant on again.

I spoke recently with a young graduate student in a math department who’d come from undergraduate study in physics. I like to draw connections between my interests and whatever else I come across, so I mentioned John Baez’ work on “higher gauge theory”, which takes the very geometric approach to particle physics known as gauge theory and “categorifies” it. It’s a very interesting program, and I hope to talk more about it here.

The student, however, waved his hands and dismissed all discussion. I pointed out that the paper Baez wrote with Urs Schreiber — who run The n-Category Café along with David Corfield — gives a beautiful explanation of a thereto ad hoc “fake flatness” condition in other approaches to extending gauge theory. I know from conversations with other mathematicians this student had spoken to that he’s interested in just this sort of extension, so why the complete disinterest? “String theory has already done all this.”

String theory, as many popular articles and books have explained, moves from the basic premise that instead of being little points the fundamental particles are all tiny vibrating “strings” of energy. From this hypothesis flows a vast theoretical model that many people think will ultimately be the “Theory of Everything” uniting all of fundamental physics the way Newton’s theory of gravity united terrestrial and celestial mechanics so long ago.

The operative word here, though, is think. String theory provides a sweeping vision of physics and a rich loam of mathematical conjectures, but the vision remains on the horizon and the conjectures stand unproven. “No matter,” say the string theorists, “It’s obvious that the math works this way because this is how it should work.” Except mathematics doesn’t work with “should”.

Here is the metaphor I return to again and again in conversation: a mathematician and a physicist walk along a sidewalk and come upon a crack in the pavement. The physicist notes the crack is only a millimeter wide and steps over it without a second thought. The mathematician (possibly afflicted with ADHD) decides to stop and peer into the crack, finding it to be many kilometers deep. The physicist rushes ahead and makes many grand predictions which turn out to be true with startling accuracy while the mathematician lags behind, carefully plastering up the crack.

This is all well and good, and the accurate predictions of physical theories like quantum electrodynamics (“QED”) have more than justified pushing ahead while the foundations are shored up from behind. String theory, though, suffers from the fact that it makes no new predictions, and has even ventured into an intellectual territory known as “the landscape” which leaves so many choices that no real predictions are possible. It’s like arguing with an astrologer. If one choice is refuted there are literally millions of infinities of alternate choices for them to fall back on. All that’s left is a fertile ground of mathematical conjecture.

So here’s where the problem really begins: string theory has grown like kudzu, and is choking the life out of fundamental physics. The more popular it gets the harder it is to get funding for alternative theories like loop quantum gravity (so much for the government’s commitment to presenting all sides of a scientific debate). The harder it is to get funding, the less likely it is that new physicists will go into those areas. The fewer new physicists entering alternate fields the more popular string theory becomes. And around and around and around in a vicious circle. The feedback loop is even used by some string theorists as a kind of evidence! “See what a large fraction of the papers on the high-energy physics theory arXiv deal with string theory? Obviously it’s correct if so many people believe it!”

And here’s where it really gets sinister: since all that’s left in string theory is a fertile ground of mathematical conjectures, some string theory zealots are turning their eyes on mathematics to invade. “Peer review is so slow and holds up progress. All papers should just be put on the math arXiv and forget the journals.” Who cares about being able to check someone’s work? Who cares about the well-known effect in journalism that few people who read today’s big story ever hear about tomorrow’s retraction?

One of the scariest discussions I ever had with a young, gung-ho string theorist was about the Atiyah-Singer Index Theorem. This is possibly one of the most beautiful results of the 20th century, and one of the more complicated to prove. About 25 years after it was first proved a “string theory proof” emerged, which was much shorter and established most cases physicists care about. I’ve seen such a “proof” of ASIT and while it did fit onto three pages it was riddled with holes from a mathematician’s perspective. In the discussion I was using this contrast as an example of how mathematical results suggested by string theory could be much more difficult to rigorously pin down. His response chilled me: “maybe it’s time mathematics started accepting string theory proofs as valid.”

String theory is a fascinating model and a wellspring of mathematical conjecture, but as it stands it is not physics. Those who rabidly hold the party line that string theory is a — is the — model of fundamental physics use that as an axiom and will not hear dissent. I’ve seen enough electronic blood shed at Peter Woit’s Not Even Wrong and his main vilifier’s site (to which I will not link) to know that there are many string theorists who have completely drained their Kool-Aid and become fanatics in the service of this ideology.

And so string theory has gonerisks going from a possible model of fundamental particles to a close-minded fundamentalist physics.

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??? What does Strings in Physics have to do with Math proofs? Do they introduce different inference rules or something? Is there someone at the math department door with an imprimatur so that proofs won’t even be examined from outside? This doesn’t sound normal.

I may have been unclear. By a “string theory proof” I don’t mean “a proof within string theory”. I mean something which is not a mathematical proof: an indication, using physics intuition, of why a certain formal mathematical statement should be true.

String theory “proofs” are arguments for certain mathematical statements, but they don’t rise to the level of rigor currently required in mathematics. He was making a normative statement that mathematicians should reduce the standards of rigor in their work to allow the sort of hand-waving physicists do to count.

Who are these people? I’m not doubting that some people might have said things along these lines, but I can’t imagine anyone I know saying something like “maybe it’s time mathematics started accepting string theory proofs as valid.”

There are very few people who I can imagine saying something like “Obviously it’s correct if so many people believe it!” either.

I certainly can’t claim to know everybody in string theory — far from it. I guess maybe I can imagine someone just starting out having such an attitude in a bit of immature youthful enthusiasm, but those people generally do grow up. I’ve been around a fair bit, and these statements seem in rather stark contrast to my personal experience.

I agree that youth has something to do with it, but it feels darker than just “enthusiasm”. I would rather not out people whom I’ve quoted here in the hopes that they grow up a bit. Suffice it to say that everything I’ve quoted directly has been said to me face-to-face, as near to the word as I can recall.

On the other hand, I’m not sure that “growing up” leads to much more than an ability to speak more diplomatically. I don’t have my copies of Brian Greene’s books around at the moment for a direct citation, but he does refer to string theory as “the model of fundamental physics”, with a definite emphasis on the definite article. I find it especially troubling that he does so despite knowing full well that there is nothing definite about the matter. He’s far from the only “mature” string theorist I’ve heard make such statements, either. There is still an undercurrent of exclusivity in a lot of what I see written about string theory.

As for the distinction between “physics proof” and “string theory proof”, I’ve seen an argument for ASIT referred to as the latter a number of times. I don’t see that it matters much, though — the assertion that mathematics should accept such things as mathematically valid despite glaring holes in their rigor is disturbing no matter what label you attach to them.

One thing I will retract for having stated more strongly: my closing sentence. I should have written it in more of a hypothetical mood than I did.

The distinction was between “string theory proof’ and “field theory proof”, not “physics proof”. But I’ll reiterate that I can’t imagine anyone saying that mathematicians should accept such proofs as valid (at least until the underlying fundamental objects have been rigorously defined.)

And, of the people I talk to, I don’t know of a single one who would dogmatically insist that string theory is the right answer.

Perhaps you could elaborate a bit further on what you mean by “ruining it” in your previous response? Are you saying that you’re forced by the behavior of a few people to make broad and false generalizations about the character of an entire field?

No, I’m saying that the behavior of a vocal minority can ruin the image of the whole group. Not all Christians are creationist flat-earthers. Not all Muslims want to enact Sharia. Not all string theorists are close-minded and seek to stifle all opposing voices.

The simple fact, though, is that there are such string theorists, and I see little, if any, ecumenical outreach from the silent majority to show that they don’t tacitly condone this sort of behavior.

Aaron: One easy thing would be to stop using the definite article, as in “the model of particle physics”. The phrasing casually dismisses all other alternatives. Stop writing it and saying it. Stop using it when speaking to reporters in the popular media. If, as you say, nobody is absolutely sure that string theory is the right answer then make sure you don’t casually speak as if it were.

babi: Go back and read again. I didn’t say it wasn’t useful as a source of mathematical conjectures. To the contrary, that’s about all it has yielded. I didn’t say it wasn’t a valid enterprise, either. I’m pointing out the tendency for a small vocal minority to become zealots.

And yes, we are exploring alternatives to dark matter, and various explanations of what dark matter might be. The biggest difference between string theory and dark matter is that dark matter actually has some experimental evidence in its favor — Bullet cluster.

I just did a search of The Elegant Universe using google, and it finds no instance of that phrase. The Fabric of the Cosmos isn’t available for searches, unfortunately. Can you be more specific, maybe?

On the other hand, there’s a difference between thinking that the other approaches to quantum gravity are wrong and thinking that string theory must be right. Most people that I know of who have looked into these alternatives have been very unimpressed.

Aaron: I’ll find a more accurate quote as soon as I have the books back sometime in March.

As for people being unimpressed with alternatives, many proponents of alternative theories are unimpressed with string theory. They don’t, however, use the definite article in describing their models’ relations with physical reality. If you really mean what you said — that you “don’t know of a single one who would dogmatically insist that string theory is the right answer” — then why do they get to use a phrasing whose semantics imply that it is exactly that?

babi: yes, there are alternative explanations. What I see written about dark matter is universally along the lines of, “our (heretofore stunningly accurate) models show there should be this much baryonic matter but our cosmological observations show that there’s a lot more ‘stuff’ out there than that. While we’re figuring it out, we’ll refer to that discrepancy as ‘dark matter’.” It’s an expression of a lack of information — a “known unknown”.

String theory, on the other hand, only makes predictions in two cases: things we cannot hope to observe on any reasonable timescale, and things that we’ve already seen and that the Standard Model already accounts for.

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